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A quantity of $7.480 \mathrm{g}$ of an organic compound is dissolved in water to make $300.0 \mathrm{mL}$ of solution. The solution has an osmotic pressure of 1.43 atm at $27^{\circ} \mathrm{C} .$ The analysis of this compound shows that it contains 41.8 percent $\mathrm{C}, 4.7$ percent $\mathrm{H}, 37.3$ percent O, and 16.3 percent $\mathrm{N}$. Calculate the molecular formula of the compound.

$$\mathrm{C}_{15} \mathrm{H}_{20} \mathrm{O}_{10} \mathrm{N}_{5}$$

Chemistry 102

Chapter 12

Physical Properties of Solutions

Solutions

Rice University

University of Kentucky

University of Toronto

Lectures

03:58

In chemistry, a solution is a homogeneous mixture composed of two or more substances. The term "solution" is also used to refer to the resultant mixture. The solution is usually a fluid. The particles of a solute are dispersed or dissolved in the solvent. The resulting solution is also called the solvent. The solvent is the continuous phase.

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All right, so in this problem, we want to find the formula for dessert. Ghani company. Uh, to do that first, we need to find more mess. So that will be the first step in this problem. And then the second step is using the molar mass. And those percentages we're gonna break down that Ah Moeller mess by Adam and computing in computing the number of malls, we will find the former. Okay, so let's go through it first. How do we find more mess? We know that we have ah ah, osmotic pressure for a given volume and then given temperature. And we know that that depends on concentration. So to be more clear, let's right the former So there was modest pressure is equal the concentration times, the gas constant times temperature. Okay, let's expend this because we know the concentration. This is mull per leaders will be number of months that all represent with the lower end. Don't be divided by, um the volume. Safety times are times deep. Okay, so that's our reform. And actually, we know the volume that was given its 0.3 litres, right, 300 milliliters are we Look up temperature is given, and we know the osmotic pressure. So we have everything that we need to compute the number of months. So that's the first step. Okay, so let's go ahead. The number of malls, Let's do some algebra rearranged DNA. Be pipe times V divided by rt. That's right. Let's plug those numbers in. So have 1.438 p m. Times divine, which is I'm converting to leaders already. The problem give us in middle letters. Okay, so let's divide it by the gas constant. I'm gonna use the point old 82 a. T m. Later for calving promote cake. And finally, the temperature, which is, um, 27 Celsius. So there will be 300 Kelvin. Cool. 300 Calvin. So let's check our units, leaders, letters. A Tim Calvin also goes away, and we're left with most That will go all the way up. And that's our final union, as we expect. Okay, so during this little math, you should get 174 Okay, 0.0 17 for most great. So now we gotta compute the more mess. Okay, So the molar mass, I'm going to represent that as I am with the bar is equal the number or the mass so little him over in a number of months. So we know the mass that was given in a problem. We know the mass of the door again in Kampe, and we know the number of most because we just computed that. So All right, that's great. So the mass is 7.4 a zero grams and the number of moles right there just computed it. Cool. Doing this, you should find the our more mass is 429.9 grams promote. So that's the first part of the problem. We're done now to the second port. Let's break now, this number by element. So let's say we're gonna work with one mole, and we know the one more contains 429 0.9 grams off the substance. And I'm gonna make a little table here for a carbon, hydrogen, oxygen and nitrogen. And we're gonna fill this table with the percentages with the amount in grams and the amount in moles. Kid three Collins here. So the percentages are given oreta and the problem. So carbon is 41.8. Hydrogen is 4.7. Oxygen is 37.3 and nitrogenous 16.3. Those percentages are in mass again. So I want to know now how much off these number here is each element. So you don't. You would take each of these numbers percentages multiplied by that together. Second column, which is the math off the element inside one mole of this substance. So doing this for carbon you will find 179.7 grams hydrogen, 20.20 oxygen. You should find 160.3 in 1970 0.7 Now, the last step is taking this numbers here. Those numbers are you know, the mass inside one more and let's convert that two number of most Okay, So we will have How many moles of carbon are inside? One more of the substance. Okay, so doing this. So divide this by 16 or Sorry. 12 more minutes of Carmen. You have 15 divided by one. You have approximately. I'm rounding this. Of course running the to the closest integer this you divide by 16 you will get 10 And this you divide by 14 you get more or less five Great So you know the inside. One more with the substance. You have 15 moles of carbon, 20 moles of hydrogen, 10 moles of oxygen, five moles of nitrogen. Therefore, you have determined the former for a new species. Okay? And Fife and that's it.

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